Energy and Power in an Electric Circuit

Energy is the ability to do work.

Power is the rate at which energy is used.

Power, symbolized by P, is a certain amount of energy used in a certain length of time, expressed as follows:

 Power =    
                 

Energy is measured in joules (J), time is measured in seconds (s), and power is measured in watts (W). 

 Energy in joules divided by time in seconds gives power in watts. 

 One watt is the amount of power when one joule of energy is used in one second.

Power in Electric Circuits

 In addition to voltage and current, another important parameter in an electric circuit is power. Power is the time rate of expending or absorbing energy.

                    

                  P = V I                                                                                

Power is the combination of both voltage and current in a circuit. Remember that voltage is the specific work (or potential energy) per unit charge, while current is the rate at which electric charges move through a conductor. We can get an equivalent expression for power by substituting for voltage and current from ohm's law.

                   P =   

                   P = I²R      

In an open circuit, where voltage is present between the terminals of the source and there is zero current, there is zero power dissipated, no matter how great that voltage may be. Since P=VI and I=0 and anything multiplied by zero is zero, the power dissipated in any open circuit must be zero. Likewise, if we were to have a short circuit constructed of a loop of superconducting wire (absolutely zero resistance), we could have a condition of current in the loop with zero voltage, and likewise no power would be dissipated.    

Power flow in an electrical device may be positive or negative. Some devices called passive components or loads; 'consume' electric power from the circuit, converting it to other forms of energy. Some devices called active devices or power source convert  from some other type of energy, such as mechanical energy or chemical energy to electric energy. Some devices can be either a source or a load, depending on the voltage and current through them, for example, a rechargeable battery. 

Electric power flowing out of a circuit into a component is arbitrarily defined to have a positive sign, while power flowing into a circuit from a component is defined to have a negative sign. Thus passive components have positive power consumption, while power sources have negative power consumption.

The Kilowatt-hour (kWh) Unit of Energy

 Since power is the rate at which energy is used, power utilized over a period of time represents energy consumption.  If you multiply power and time, you have energy.

W = Pt

When you pay your electric bill, you are charged on the basis of the amount of energy you use, not the power.  Because power companies deal in huge amounts of energy, the most practical unit is the kilowatt-hour. You use a kilowatt-hour of energy when you use one thousand watts of power for one hour.  For example, a 100 W light bulb burning for 10 h uses 1 kWh of energy.

 W = Pt = (100 W) (10 h) = 1kWh

                                                      

Problem Solving                                                                                           

Example 1

Calculate the power in each of the three circuits of Figure 1.

Figure 1.

Solution

In circuit (a), V and I are known.  Therefore, use Equation (1-8).

 P = VI = (10 V)(2 A) = 20 W

In circuit (b), I and R are known.  Therefore, use Equation (1-9).

 P = I²R = (2 A) ²(47W) = 188 W

In circuit (c), V and R are known.  Therefore, use Equation (1-10).

 P = = = 2.5 W